What is (a+1)/b =(a-1)/b+(b+1)/a ?

The solution to (a+1)/b =(a-1)/b+(b+1)/a is Parabola with (h,k)=(-1/8 ,-1/2),p= 1/2

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(a+1)/b =(a-1)/b+(b+1)/a

\frac{a + 1}{b} = \frac{a - 1}{b} + \frac{b + 1}{a}

(h, k) = (- \frac{1}{8}, - \frac{1}{2}), p = \frac{1}{2}

Solution steps

\frac{a + 1}{b} = \frac{a - 1}{b} + \frac{b + 1}{a}

Rewrite

\frac{a + 1}{b} - \frac{a - 1}{b} - \frac{b + 1}{a} = 0

in the standard form

4 \cdot \frac{1}{2} (a - (- \frac{1}{8})) = (b - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{8}, - \frac{1}{2}), p = \frac{1}{2}

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1

y^{2} - y - x + 1 = 0

\frac{( x - 5 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{16} = 1

x^{2} = 6 y

\frac{( y - 3 ) ^{2}}{11} - \frac{( x + 1 ) ^{2}}{5} = 1

What is (a+1)/b =(a-1)/b+(b+1)/a ?
The solution to (a+1)/b =(a-1)/b+(b+1)/a is Parabola with (h,k)=(-1/8 ,-1/2),p= 1/2